Conventional servo track ID demodulators for hard disk drives (HDD) implement simple (i.e., 1-D) digital filters. Such simplistic digital filters have poor signal to noise ratio (SNR). However, as signal to noise ratios decrease with improving read channels, it becomes necessary to improve the SNR capability of the digital filters and therefore servo track ID demodulators.
Referring to FIG. 1, a typical 4 tap finite impulse response (FIR) filter 10 is shown. The filter 10 includes delay elements 12a-12n, multipliers 14a-14n and a summation circuit 16. The delay elements 12a-12n delay the sampled input signal IN. Each of the delay element signals is then presented to the multipliers 14a-14n. An output of each of the multipliers is then presented to the summation circuit 16. The summation circuit 16 presents the output signal OUT. The filter 10 has an output/input transfer function of:OUT/IN=K1+K2D+K3D2+K4D3 
Some typical servo track ID demodulators do not implement digital filters. By not implementing digital filters the SNR of the track ID signal is typically about 3.5 dB better than using differentiation. However, implementations without digital filters are susceptible to DC offsets and thermal asperity.